The invention relates to radar tomography, according to which unknown material properties, in particular electromagnetic properties, of an object shall be measured. The concept of radar tomography is generally known, for instance from A. E. Bulyshev et al. “Three-dimensional vector microwave tomography: theory and computational experiments”, Inverse Problems, August 2004, Z. Q. Zhang et Q. H. Liu. “Three-Dimensional Nonlinear Image Reconstruction for Microwave Biomedical Imaging”, IEEE Transactions on Biomedical Engineering, March 2004, D. W. Winters et al., “Three-Dimensional Microwave Breast Imaging: Dispersive Dielectric Properties Estimation Using Patient-Specific Basis Functions”, IEEE Transactions on Medical Imaging, July 2009, and Q. Fang et al., “Microwave Image Reconstruction From 3-D Fields Coupled to 2-D Parameter Estimation”, IEEE Transactions on Medical Imaging, April 2004.
The object, e.g. a patient or tissue material, is placed in an area surrounded by antenna elements (generally, by transmitters). The area can have the form of a cuboid or a cylinder for example. The region of interest of the object, in which the material properties shall be determined, is divided into a mesh. The actual tomography includes two main elements. The first element is a forward solver in which the complex electromagnetic fields at all the elements of the mesh are determined. The second element is an inverse solver in which the unknown material properties of the object are computed from the complex electromagnetic fields. Each of these processes is done once or repeated sequentially several times until the desired accuracy of the results is achieved.
The complexity of a radar tomography device mainly depends on the density of the mesh (number of elements or regions in the mesh, e.g. pixels or voxels), the operating dimensions (1D, 2D or 3D) and the number of transmitters and receivers (or transceivers). Considering for example a cubic region of dimensions 15×15×15 cm3 and dividing it into 100×100×100 voxels or 1 million elements, determining the 3D components of the complex field at all the voxels requires resolving for 3×1 million or 3 million variables. If the complex electromagnetic field is approximated by a scalar, as done in many state of the art algorithms, the number of variables drops back to 1 million. These numbers have to be resolved in both the forward and backward solvers for each transmitted signal. Hence, the complexity of the problem increases dramatically with the increase in the mesh density and the number of transceivers used.
To limit the complexity in radar tomography, an obvious solution is trying to reduce the density of the mesh by having larger mesh elements (i.e. a more coarse grid). However, this solution also reduces the quality of the obtained result (e.g. of an image reconstructed from the determined material properties). Another obvious solution is trying to limit the meshed area to the object or the region of interest, but this solution still has high complexity, especially in 3D, unless the dimension of the mesh elements (i.e. voxel size) is also large.